Global Aspects of 3-Form Fields in Axion Yang-Mills Systems

Generalized symmetries have proved crucial for understanding quantum fields. In this talk, I highlight the role of higher-form symmetries within the axion Yang-Mills theory. This system exhibits an emergent 2-form symmetry, which must be gauged to satisfy certain 't Hooft anomaly matching conditions. The resulting 3-form gauge theory provides a compelling description of the infrared dynamics of axion domain walls. It also captures the interplay between the light axion and the heavier hadronic degrees of freedom.  Time permitting, I will discuss how the global structure of the ultraviolet gauge group determines whether the system supports an IR fractional quantum Hall state on the axion domain walls.